1. Field of the Invention
The present invention relates to a semiconductor device with a new structure.
2. Description of the Related Art
A diode has been known to have a pn or pin junction structure. With respect to a current-voltage characteristic of the diode, a characteristic that electric current increase when an applied voltage increases and a characteristic that electric current decrease when an applied voltage decreases show identical characteristics. Especially, the diode does not show a hysterisis characteristic in a current-voltage characteristic.
The inventors of the present invention formed a device having a quantum-wave interference layer which reflects quantum-waves and a middle layer which does not have a multi-period structure but has a plane structure in a band structure, where the quantum-wave interference layer and the middle layer are connected in series, and measured a current-voltage characteristic of the device. The current-voltage characteristic of the device shows that when an applied voltage increases in a forward direction, an electric current rises abruptly at a certain value of voltage with a step function. Also, the current-voltage characteristic of the device shows that when an applied voltage decreases in a backward direction from the region where the electric current increases first, the electric current decreases at a certain value of voltage, which is different from the value described above, with a step function. In short, a hysterisis characteristic that the device has different value of voltage when the electric current rises and decreases abruptly with a step function, or when the current-voltage characteristic varies with a step function can be found.
It is, therefore, an object of the present invention to provide a semiconductor device with a new structure using this hysterisis characteristic. The semiconductor device in the present invention utilizes a hysterisis of the current-voltage characteristic which varies with a step function, and can be applied to Schmitt circuit and a binary element. That is, the device which does not show chattering with respect to a condition variation can be provided.
In the light of these objects a first aspect of the present invention is a semiconductor device which is constituted by a quantum-wave interference layer units having plural periods of a pair of a first layer and a second layer, the second layer having a wider band gap than the first layer, and a middle layer disposed between adjacent two of the quantum-wave interference layer units. Each thickness of the first and the second layers is determined by multiplying by an odd number one fourth of a quantum-wave wavelength of carriers in each of the first and the second layers. Plural units of the quantum-wave interference layers are formed with a middle layer, which does not have a multi-period structure but has a plane band structure, lying between each of the quantum-wave interference units.
The second aspect of the present invention is to set a kinetic energy of the carriers, which determines the quantum-wave wavelength, at the level near the bottom of a conduction band when the carriers are electrons or at the level near the bottom of a valence band in the second layer when the carriers are holes.
The third aspect of the present invention is to define each thickness of the first and the second layers as follows:
DW=nWxcexW/4=nWh/4[2mW(E+V]xc2xdxe2x80x83xe2x80x83(1)
and
DB=nBxcexB/4=nBh/4(2mBE)xc2xdxe2x80x83xe2x80x83(2)
In Eqs. 1 and 2, h, mW, mB, E, V, and nW, nB represent Plank""s constant, the effective mass of carrier conducting in the first layer, the effective mass of carriers in the second layer, the kinetic energy of the carriers at the level near the lowest energy level of the second layer, the potential energy of the second layer relative to the first layer, and odd numbers, respectively.
The fourth aspect of the present invention is a quantum-wave interference layer having a partial quantum-wave interference layers Ik with arbitrary periods Tk including a first layer having a thickness of nWkxcexWk/4 and a second layer having a thickness of nBkxcexBk/4 for each of a plural different values Ek, Ek+V. Ek, Ek+V, xcexBk, xcexWk, and nBk, nWk represent a kinetic energy of carriers conducted in the second layer, a kinetic energy of carriers conducted in the first layer, a quantum-wave wavelength corresponding energies of the second layer and the first layer, and odd numbers, respectively.
The fifth aspect of the present invention is to form a middle layer having narrower bandwidth than that of the second layer.
The sixth aspect of the present invention is to form a middle layer having half a thickness of its quantum-wave wavelength xcexB.
The seventh aspect of the present invention is to form a xcex4 layer between the first layer and the second layer, which sharply varies energy band at the boundary between the first and second layers and is substantially thinner than that of the first and the second layers.
The eighth aspect of the present invention is a semiconductor device having a pin junction structure, and the quantum-wave interference layer and the middle layer are formed in the i-layer.
The ninth aspect of the present invention is to form the quantum-wave interference layer and the middle layer in the n-layer or the p-layer.
The tenth aspect of the present invention is a semiconductor device having a hysterisis characteristic as a current-voltage characteristic.
The principle of the semiconductor device of the present invention is explained hereinafter. FIG. 1A shows an energy diagram of a conduction band and a valence band when an external voltage is applied to the interval between the p-layer and the n-layer in a forward direction. As shown in FIG. 1A, the conduction band of the i-layer becomes plane by applying the external voltage. Four quantum-wave interference layer units Q1 to Q4 are formed in the i-layer, and middle layers C1 to C3 are formed at each intervals of the quantum-wave interference layer units. FIG. 2 shows a conduction band of a quantum-wave interference layer unit Q1 having a multi-layer structure with plural periods of a first layer W and a second layer B as a unit. A band gap of the second layer B is wider than that of the first layer W.
Electrons conduct from left to right as shown by an arrow in FIG. 2. Among the electrons, those that exist at the level near the lowest energy level of a conduction band in the second layer B are most likely to contribute to conduction. The electrons near the bottom of conduction band of the second layer B has a kinetic energy E. Accordingly, the electrons in the first layer W have a kinetic energy E+V which is accelerated by a potential energy V due to the band gap between the first layer W and the second layer B. In other words, electrons that move from the first layer W to the second layer B are decelerated by potential energy V and return to the original kinetic energy E in the second layer B. As explained above, kinetic energy of electrons in the conduction band is modulated by potential energy due to the multi-layer structure.
When thicknesses of the first layer W and the second layer B are equal to order of quantum-wave wavelength, electrons tend to have characteristics of a wave. The wave length of the electron quantum-wave is calculated by Eqs. 1 and 2 using kinetic energy of the electron. Further, defining the respective wave number vector of first layer W and second layer B as KW and KB, reflectivity R of the wave is calculated by:
R=(|KW|xe2x88x92|KB|)/(|KW|+|KB|)
=([mW(E+V)]xc2xdxe2x88x92[mBE]xc2xd)/([mW(E+V)]xc2xd+[mBE]xc2xd)
=[1xe2x88x92(mBE/mW(E+V))xc2xd]/[1+(mBE/mW(E+V))xc2xd]xe2x80x83xe2x80x83(3).
Further, when mB=mW, the reflectivity R is calculated by:
R=[1xe2x88x92(E/(E +V))xc2xd]/[1+(E/(E +V))xc2xd]xe2x80x83xe2x80x83(4).
When E/(E+V)=x, Eq. 6 is transformed into:
R=(1xe2x88x92xxc2xd)/(1+xxc2xd)xe2x80x83xe2x80x83(5).
The characteristic of the reflectivity R with respect to the energy ratio x obtained by Eq. 5 is shown in FIG. 3.
And when the second layer B and the first layer W have a s-layers structure, the reflectivity Rs of an incident plane of the quantum-wave is calculated by:
Rs=[(1xe2x88x92xs)/(1+xs)]2xe2x80x83xe2x80x83(6).
When the condition xxe2x89xa61/10 is satisfied, Rxe2x89xa70.52. Accordingly, the relation between E and V is satisfied with:
Exe2x89xa6V/9xe2x80x83xe2x80x83(7).
Since the kinetic energy E of the conducting electrons in the second layer B exists near the bottom of the conduction band, the relation of Eq. 7 is satisfied and the reflectivity R at the interface between the second layer B and the first layer W becomes 52% or more. Consequently, the multi-layer structure having two kinds of layers with band gaps different from each other enables to reflect quantum-wave of electrons, which conduct in an i-layer, between the first and second layers.
Further, utilizing the energy ratio x enables the thickness ratio DB/DW of the second layer B to the first layer W to be obtained by:
DB/DW=[mW/(mBx)]xc2xdxe2x80x83xe2x80x83(8).
As shown in FIG. 2B, when the forward voltage is applied to the device having quantum-wave interference layer in the i-layer, the energy level of the quantum-wave interference layer band inclined by the external voltage. Then E+V and E, or kinetic energy of the electrons in the first layer W and the second layer B respectively, increase according to a proceeding of quantum-wave. Accordingly, the thicknesses of the first layer W and the second layer B no longer improve the quantum-wave reflectivity of the electrons injected into the i-layer. Consequently, in the range of applied voltage for which the kinetic energy of electrons does not exceed the energy level used to design the thickness of the quantum-wave interference layer, the electrons are reflected and do not cause electric current. But when the applied voltage increases to the degree that the kinetic energy of the electrons injected into the i-layer exceeds the energy level used to design the thicknesses of the quantum-wave interference layer, reflected electrons begin to flow rapidly. Consequently, I-V characteristic of the diode varies rapidly. In short, the dynamic resistance of the diode drops.
As described later, this diode has a current-voltage characteristic that the values of voltage are different when the electric current rises and decreases abruptly, as shown in FIG. 8. In short, it was found that the current-voltage characteristic of the diode shows a hysterisis characteristic.
Although the reason why the current-voltage characteristic of the diode show a hysterisis characteristic is not clear in the present stage, it is considered as following. FIGS. 4A to 4D show energy diagrams of a conduction band of an nip structure: FIG. 4A shows an energy diagram when an external voltage is 0 V; FIG. 4B shows when a voltage is applied at a point that electric current begins to rise abruptly; FIG. 4C shows when a voltage increases abruptly and a large electric current flows; and FIG. 4D shows when a voltage decreases gradually from the condition shown in FIG. 4C and when a voltage is applied at a point that electric current begins to decrease abruptly.
In a range of the applied voltage shown in FIGS. 4A and 4B, a condition when each thicknesses of the quantum-wave interference layers is determined by multiplying by an odd number one fourth of a quantum-wave wavelength of injected electrons is satisfied. In this condition, electrons are reflected by the quantum-wave interference layers and there is no transfer of electrons. When an external voltage is applied until an electric potential gradient becomes as shown in FIG. 4B, a reflection condition is not satisfied and electrons are conducted in the quantum-wave interference layers. Point A shown in FIG. 8 represents the condition. Because electrons are confined by each middle layers C1, C2, and C3, the middle layers C1, C2, and C3 can be defined as carrier accumulation layers. Accordingly, the bottom of a conduction band of the middle layers C1, C2, and C3 is preferably set at a level lower than the bottom of a conduction band of the second layer B. Alternatively, the bottom of the second layer B and the conduction band can be equal. But when the electrons existing in the middle layers C1, C2, and C3 increases, electrons tend to exist in higher level. Then a kinetic energy of the electrons existing in higher level increases, and electrons are not reflected by the quantum-wave interference layer units because of unsatisfaction of the reflection condition. As a result, electrons transmit the quantum-wave interference layer units Q2, Q3, and Q4 and flow toward the p-layer. An energy diagram of the conduction band when the electrons are conducted toward the p-layer is shown in FIG. 4C. Point B in FIG. 8 represents the condition.
Then a current-voltage characteristic when electric current decreases gradually is explained hereinafter. An energy diagram on conduction condition that electric current rises like a step is shown in FIG. 4C. Almost all the external voltage is applied to the certain part of the i-layer which is closer to the n-layer than the first quantum-wave interference layer unit Q1 and the certain part of the i-layer which is set closer to the p-layer than the last quantum-wave interference layer unit Q4, and an electric potential gradient is hardly found between the quantum-wave interference layer units Q1 to Q4. When the applied voltage decreases, electric current continues to flow until the electric potential gradient in the i-layer becomes equal to that shown in FIG. 4B, at the point when electric current begins to rise abruptly. This condition is shown in FIG. 4D. But because no electric potential gradient is found between the quantum-wave interference layer units Q1 to Q4, the external voltage shown in FIG. 4D is smaller than that shown in FIG. 4B. Point C in FIG. 8 indicates the voltage point described above. When the electric potential gradient is as shown in FIG. 4D, a quantum-wave wavelength of injected electrons satisfies a reflection condition, and the electric current decreases like a step. As a result, hysterisis is occurred is a current-voltage characteristic.
Because a forward voltage is applied to the semiconductor device, low-voltage drive become possible and insulation separation between elements becomes easy. And because it is considered that electrons are propagated in the quantum-wave interference layers as a wave at a high speed, a response velocity becomes fast.
The thicknesses of the first layer W and the second layer B are determined for selectively reflecting the holes or the electrons, because of the difference in potential energy between the valence and the conduction bands, and the difference in effective mass of holes and electrons in the first layer W and the second layer B. In other words, the optimum thickness for reflecting electrons is not the optimum thickness for reflecting holes. Equations 3-8 refer to a structure of the quantum-wave interference layer for selectively reflecting electrons. The thickness for selectively reflecting electrons is designed based on the difference in the potential energy of the conduction band and on the effective mass of electrons. Further, the thickness for selectively reflecting holes is designed based on the difference in the potential energy of the valence band and on the effective mass of holes, forming another type of quantum-wave interference layer in an i-layer for reflecting only holes and allowing electrons to pass through.
Accordingly, a quantum-wave interference layer unit which reflects holes and functions as a reflective layer to holes can be formed to connect in series to each quantum-wave interference layer units described above, which reflects only electrons.
The semiconductor device described above having a quantum-wave interference layer unit can have a state not to occur electric current by reflecting carriers selectively in a range of 0 V to a certain value of a bias voltage. Accordingly, the semiconductor device can be formed by only one of the n-layer and the p-layer in which the quantum-wave interference layer units and the middle layer are formed. Alternatively, the semiconductor device can be formed by a pn junction structure, in which the quantum-wave interference layer units and the middle layer are formed.
The quantum-wave interference layer was formed in the i-layer, which is placed between the n-layer and the p-layer of the semiconductor device having an nip structure. Alternatively, the quantum-wave interference layer can be formed in a semiconductor device having only n-layers or p-layers. Further alternatively, a quantum-wave interference layer which reflects electrons and a quantum-wave interference layer which reflects holes can be arranged in series.
Forming the quantum-wave interference layer of electrons in the p-layer and that of holes in the n-layer enables to vary V-I characteristic of the diode more abruptly and lower its dynamic resistance notably.
FIG. 5 shows a plurality quantum-wave units Ik with arbitrary periods Tk including a first layer having a thickness of DWk and a second layer having a thickness of DBk and arranged in series.
Each thickness of the first and the second layers satisfies the formulas:
DWk=nWkxcexWk/4=nWkh/4 [2mWk(Ek+V)]xc2xdxe2x80x83xe2x80x83(9)
and
DBk=nBkxcexBk/4=nBkh/4 (2mBkEk)xc2xdxe2x80x83xe2x80x83(10)
In Eqs. 9 and 10, Ek, mWk, mBk, and nWk and nBk represent plural kinetic energy levels of carriers conducted into the second layer, effective mass of carriers with kinetic energy Ek+V in the first layer, effective mass of carriers with kinetic energy Ek in the second layer, and arbitrary odd numbers, respectively.
The plurality of the partial quantum-wave interference layers Ik are arranged in series from I1 to Ij, where j is a maximum number of k required to form a quantum-wave interference layer as a whole. The carriers existing in a certain consecutive energy range can be reflected by narrowing a discrete intervals.
The fifth aspect of the present invention is to form the middle layer to have a band structure in which the bottom of a conduction band of the middle layer is lower than a bottom of a conduction band in the second layer B when carriers are electrons, and a band structure in which the bottom of a valence band of the middle layer is lower than a bottom of a valence band in the second layer B when carriers are holes. FIGS. 1B-E illustrate the above embodiment.
The sixth aspect of the present invention is to form the middle layer to have half a thickness of its quantum-wave wavelength xcexW. As a result, the carriers conducted in the i-layer can be confined effectively.
The seventh aspect of the present invention is to form a xcex4 layer at the interface between the first layer W and the second layer B. The xcex4 layer has a thickness substantially thinner than both of the first layer W and the second layer B and sharply varies the energy band profile of the device. The reflectivity R of the interface is determined by Eq. 5. By forming the xcex4 layer, the potential energy V of an energy band becomes larger and the value x of Eq. 5 becomes smaller. Accordingly, the reflectivity R becomes larger.
Variations are shown in FIGS. 6A to 6C. The xcex4 layer may be formed on both ends of every first layer W as shown in FIGS. 6A to 6C. In FIG. 6A, the xcex4 layers are formed so that an energy level higher than that of the second layer B may be formed. In FIG. 6B, the xcex4 layers are formed so that an energy level lower than that of the first layer W may be formed. In FIG. 6C, the xcex4 layers are formed so that a band bottom higher than that of the second layer B and a band bottom lower than that of the first layer W may be formed. As an alternative to each of the variations shown in FIGS. 6A to 6C, the xcex4 layer can be formed on one end of every first layer W.